The Homeland Security Department has set up hotlines for illegal immigrants who believe their rights under President Obama’s amnesty policy have been violated.

In a memo announcing the customer complaint line, U.S. Customs and Border Protection asked illegal immigrants to “please tell us about your experience” if they believe they were treated “contrary to the new DHS enforcement priorities.”

The department alerted “stakeholders” last week of three complaint hotlines: one for CBP, which oversees the Border Patrol; one for U.S. Immigration and Customs Enforcement, which handles immigration laws in the nation’s interior; and one for U.S. Citizenship and Immigration Services, which is poised to handle the millions of amnesty applications expected to be filed.

The amnesty policy grants tentative legal status to up to 4 million illegal immigrants and orders Border Patrol agents and Immigration and Customs Enforcement agents not to arrest other illegal immigrants who say they have been hiding in the U.S. for years but don’t meet the criteria for full amnesty.

Border Patrol agents said the complaint lines amount to a slap in the face to those who put their lives on the line to enforce the law.

“Instead of supporting our agents, this administration has decided it is more important to find new ways to solicit complaints and invite ridicule against them,” said Shawn Moran, vice president of the National Border Patrol Council, the labor union that represents line agents. “We demand that this administration spend more time defending the men and women defending our nation and less time promoting the extreme agendas of pro-illegal-immigration organizations.”

He said he would like the Homeland Security Department to set up a complaint line for agents instead, so they could register their concerns over the administration’s failure to enforce laws involving their own pay, the disparity in the firepower they bring to the fight with drug cartels and the administration’s “failure to fully enforce our immigration laws.”

Immigrant rights advocates, meanwhile, are torn over whether complaints have proved effective. Some say they are useful, but others say they rarely produce results and question the department’s ability to investigate complaints against itself.

The Homeland Security Department and CBP issued memos detailing the customer complaint lines last week. CBP’s notice included this invitation: “If you believe you (or a family member) were apprehended and processed by a Customs and Border Protection officer or Border Patrol agent contrary to the new DHS enforcement priorities, please tell us about your experience by contacting the CBP INFO Center.”

The Homeland Security memo says it expects more “questions and feedback” from the amnesty and lists all three complaint lines.

The Obama administration has tried to walk a tight line, insisting it is boosting enforcement even as the president and his political appointees at the Homeland Security Department have carved an ever-widening circle of illegal immigrants for protection in order to appease their advocates.

In the past two years, Mr. Obama has tilted toward the advocates’ position, cutting deportations 20 percent from 2012 to 2014 even as illegal crossings of the U.S.-Mexico border have increased.

In November, Mr. Obama announced an amnesty for illegal immigrant parents whose children are American citizens or legal permanent residents, granting them legal status for three years and work permits entitling them to compete for jobs. He also expanded a 2012 amnesty for illegal immigrants who came to the U.S. as children.

He also had top officials at the Homeland Security Department issue “guidance” ordering agents to generally ignore illegal immigrants who have hidden in the U.S. for some time or who claim other extenuating circumstances.

The guidance indicates that agents should not bother pursuing illegal immigrants who don’t have serious criminal records or aren’t recent illegal immigrants, meaning those who arrived in the U.S. since Jan. 1, 2014. Even immigrants convicted of domestic violence may not be “priorities” for deportation if they were also victims at some point.

Mr. Moran, testifying to a Senate committee last week, said agents now have to go through a checklist when they encounter illegal immigrants. Those who give the right answers are likely to be released.

“The messaging on the training from CBP has been inconsistent at best,” he said.

Sen. Ron Johnson, Wisconsin Republican and chairman of the Homeland Security and Governmental Affairs Committee, said it sounded as though immigrants only had to say “magic words” to avoid arrest.

During the border surge this summer, Mr. Moran said, agents discovered that some of the illegal crossers had written scripts with them to coach them on what to say to be released into the U.S.

A Homeland Security spokeswoman said the hotline memo was intended to make sure stakeholders knew where to go for information.

“This provides one place for all stakeholders to find out more about the new DHS guidelines, deferred action, eligibility for new initiatives, or to register comment or complaint,” said Ginette Magana, the spokeswoman. “DHS continuously engages with stakeholders, members of Congress and interested individuals to provide the most up-to-date information and answer questions about any new initiatives.”

“The CBP Info Center (CIC) is a toll-free service for individuals with questions about CBP procedures or who wish to register a complaint about an encounter with CBP that they believe to be contrary to guidance,” the department says on the CBP page.

The CBP page says it has only “limited assistance” available in Spanish for those calling to complain, but the complaint hotline for ICE specifically says it can handle calls both Spanish and English.

Homeland Security has had complaint lines for some time, and Mr. Obama picked a fight with Congress over an advocacy office in ICE several years ago. Congress canceled funding for the job, so Mr. Obama changed the title but kept the same person doing the same work and argued that he met the letter of the law.